Option B:
25 degrees
Solution:
Given data in triangle PQR,
The side opposite to angle P is p.
The side opposite to angle Q is q.
The side opposite to angle R is r.
q = 36, r = 20, angle Q = 50°.
To find the measure of angle R:
Using law of sine,
[tex]$\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]
[tex]$\Rightarrow\frac{p}{\sin P}=\frac{q}{\sin Q}=\frac{r}{\sin R}[/tex]
Take only two sides.
[tex]$\Rightarrow\frac{q}{\sin Q}=\frac{r}{\sin R}[/tex]
Substitute the given values.
[tex]$\Rightarrow\frac{36}{\sin 50^\circ}=\frac{20}{\sin R}[/tex]
Do cross multiplication.
[tex]\Rightarrow36\times\sin R = \sin50^\circ\times20[/tex]
sin 50° = 0.766
[tex]\Rightarrow36\times\sin R = 0.766\times20[/tex]
[tex]\Rightarrow36\times\sin R = 15.32[/tex]
[tex]$\Rightarrow\sin R = \frac{15.32}{36}[/tex]
[tex]$\Rightarrow\sin R = 0.4255[/tex]
[tex]$\Rightarrow R = \sin^{-1}(0.4255)[/tex]
⇒ R = 25.18°
⇒ R = 25° (approximately)
Option B is the correct answer.
Hence the measure of angle R is 25 degrees.
